On the many saddle points description of quantum black holes

TL;DR

This paper models semiclassical black holes using coupled Liouville theories, revealing infinite entropy and saddle point dominance, with implications for quantum states and the firewall paradox.

Contribution

It introduces a novel description of black holes via two matched Liouville theories and analyzes their saddle points, connecting to quantum states and string theory.

Findings

Black holes can be described by two Liouville theories at the horizon.

Correlation functions are dominated by two complex saddle points.

The system can be interpreted as two interacting Bose-Einstein condensates.

Abstract

Considering two dimensional gravity coupled to a CFT, we show that a semiclassical black hole can be described in terms of two Liouville theories matched at the horizon. The black hole exterior corresponds to a space-like while the interior to a time-like Liouville theory. This matching automatically implies that a semiclassical black hole has an infinite entropy. The path integral description of the time-like Liouville theory (the Black Hole interior) is studied and it is found that the correlation functions of the coupled CFT-gravity system are dominated by two (complex) saddle points, even in the semiclassical limit. We argue that this system can be interpreted as two interacting Bose-Einstein condensates constructed out of two degenerate quantum states. In AdS/CFT context, the same system is mapped into two interacting strings intersecting inside a three-dimensional BTZ black hole. Finally, we discuss why, beyond the semiclassical approximation, we expect no firewalls appearing in our system.